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Recreate DensityMatrixPlot
asked by David Tam (2022/03/27 19:10)
In Mathematica, I define the basis according to the documentation for DensityMatrixPlot:
lbasisF = With[{l = 3}, Flatten[Table[{SphericalHarmonicY[l, m, \[Theta], \[Phi]], SphericalHarmonicY[l, m, \[Theta], \[Phi]]}, {m, -l, l}]]];
Now I can construct a density matrix with some randomly chosen numbers, and make a plot:
dmF = CFDensityMatrix[3, 1, With[{vv = {0.7, 0, 0.3, 0, 0, 0.3, 0, 0, 0.1, 0.5, 0.1, 0, 0.2, 0}}, vv/Sqrt@Total[vv^2]]] DensityMatrixPlot[dmF]
However, the following superposition shows that directly plotting in the orbital basis doesn't make the same plot:
Show[ dmplot, SphericalPlot3D[ Conjugate[lbasisF].dmF.lbasisF, {\[Theta], 0, Pi}, {\[Phi], 0,(*2 Pi*)Pi} , PlotRange -> All, AspectRatio -> Automatic, AxesLabel -> {“x”, “y”, “z”}] ]
What is the right way to find the angular function as function of theta and phi, and how does DensityMatrixPlot avoid this problem?
Answers
Hello David,
Which version of Mathematica are you using?
Dear David
There is a difference between the wave function $\sqrt{1/2} (p_x + p_y)$ and the charge density of the $p_x$ and $p_y$ orbital. I here used $p$ orbitals as they are simpler than the $f$ orbitals. Have a look at the tutorial at Quanty/tutorial/wavefunctions_and_density to see the difference.
You find this tutorial in the Mathematica Help files. Go to Help → Documentation → Add ons and packages (bottom) → Quanty → Documentation → Tutorials: Wave functions and density
This might solve your question Maurits